user41725
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 Jul 2 awarded Curious Apr 14 accepted $\lim_{k\rightarrow \infty}\frac{2^k}{\gamma}\log\mathbb{E}[e^{-\gamma \frac{X}{2^k}}]$ Apr 10 revised $\rho_\gamma(X)=\frac{1}{\gamma} \log \mathbb{E}[e^{-\gamma X}]$ edited title Apr 10 asked $\lim_{k\rightarrow \infty}\frac{2^k}{\gamma}\log\mathbb{E}[e^{-\gamma \frac{X}{2^k}}]$ Apr 9 accepted $\rho_\gamma(X)=\frac{1}{\gamma} \log \mathbb{E}[e^{-\gamma X}]$ Apr 9 comment $\rho_\gamma(X)=\frac{1}{\gamma} \log \mathbb{E}[e^{-\gamma X}]$ makes sense, thanks for your help and patience Apr 9 comment $\rho_\gamma(X)=\frac{1}{\gamma} \log \mathbb{E}[e^{-\gamma X}]$ would you please elaborate a bit on the fact that the inequality is strict for all non constant X. ( almost surely ). Thanks in advance! Apr 9 comment $\rho_\gamma(X)=\frac{1}{\gamma} \log \mathbb{E}[e^{-\gamma X}]$ Thanks! Am I assuming correctly that you used Jensen en.wikipedia.org/wiki/Jensen's_inequality $\frac{1}{\gamma}\log\mathbb{E}[e^{-\gamma 2 X}] \geq \frac{1}{\gamma}\log(\mathbb{E}[e^{-\gamma X}])^2$ Apr 9 revised $\rho_\gamma(X)=\frac{1}{\gamma} \log \mathbb{E}[e^{-\gamma X}]$ edited tags Apr 9 asked $\rho_\gamma(X)=\frac{1}{\gamma} \log \mathbb{E}[e^{-\gamma X}]$ Apr 9 awarded Benefactor Apr 9 comment $f(z):=\int_{\mathbb{R}} \frac{1}{t-z} d\mu(t)$ show $\lim_{y\rightarrow 0}iyf(iy)=-\mu(\lbrace 0 \rbrace)$ thanks so much! Apr 9 accepted $f(z):=\int_{\mathbb{R}} \frac{1}{t-z} d\mu(t)$ show $\lim_{y\rightarrow 0}iyf(iy)=-\mu(\lbrace 0 \rbrace)$ Apr 5 awarded Tumbleweed Apr 1 awarded Promoter Apr 1 comment $f(z):=\int_{\mathbb{R}} \frac{1}{t-z} d\mu(t)$ show $\lim_{y\rightarrow 0}iyf(iy)=-\mu(\lbrace 0 \rbrace)$ Thanks again, but I have one more question. I don't understand the last equality, it is a bit too fast for me to see this. Could you perhaps explain that last step, please? Mar 26 asked $f(z):=\int_{\mathbb{R}} \frac{1}{t-z} d\mu(t)$ show $\lim_{y\rightarrow 0}iyf(iy)=-\mu(\lbrace 0 \rbrace)$ Feb 19 asked conversion of number from base 10 to base 16 Feb 13 awarded Commentator Feb 13 comment zeta function and probability divisible by k and choosing squares but the "P" in the sum should be small p, right?